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GENERALIZED BOCHNER'S THEOREM FOR RADIAL FUNCTION 被引量:5
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作者 Wu Zongmin (Fudan University, China) 《Analysis in Theory and Applications》 1997年第3期47-57,共11页
A radial function can be expressed by its generator through The positive definite of the function plays an important rote in the radial basis interpolation. We can naturally use Bochner's Theorem to check if is po... A radial function can be expressed by its generator through The positive definite of the function plays an important rote in the radial basis interpolation. We can naturally use Bochner's Theorem to check if is positive definite. This requires however a n-dhnensiotial Fourier transformation and it is not very easy to calculate. Furthermore in a lot of cases we will use for spaces of various dimensions too, then for every fixed n we need do the Fourier transformation once to check if the function is positive definite in the n-di-mensional space. The completely monotone function:, which is discussed in [4] is positive definite for arbitrary space dimensions. With this technique tve can very easily characterize the positive definite, of a radial function through its generator. Unfortunately there is only a very small subset of radial function which is completely monotone. Thus this criterion excluded a lot of interesting functions such as compactly supported radial function, whcih are very useful in application. Can we find some conditions (as the completely monotone function) only for the \-dimen simial Fourier transform of the generator epto characterize a radial function 9, which is positivedefinite in n-dimensional (fixed n) spacel In this paper we defined a kind of incompletelymonotone function of order a, for a= 0,,1/2 ,1,3/2,(we denote the function class by ICM) ,in this sence a normal positvie function is in ICM a positive monotone decreasing function is inICM and a positive monotone decreasing and convex function is in ICM2- Based on this definition we get a generalized Bochner's Theorem for radial function-. If dimensional Fouriertransform of the generator of a radial function can be written as , then corre-spending radial function (x) is positive definite as a n-variate function iff F is an incomplete-ly monotone function of order a= (n- 1 )/2 (or simply In this way we have characterized the positive definite of the radial function as a n-vari-ate function through its generator in the sense of the Bocher's Theorem. 展开更多
关键词 generalized BOCHNER’s theorem FOR RADIAL FUNCTION very
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A Generalized Form of Whitney's Theorem
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作者 CEN Yan-ming CEN Li-hui 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第1期75-78,共4页
Whitney's theorem is a famous theorem in the local singularity theory. In this paper, as an application of Malgrange preparation theorem, a generalized form of Whitney's theorem will be derived.
关键词 generalized of Whitney's theorem
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Generalized S-KKM Theorems and Minimax Inequalities in FC-Spaces
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作者 张红玲 范翠丽 《Journal of Southwest Jiaotong University(English Edition)》 2008年第3期303-307,共5页
The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is t... The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value. 展开更多
关键词 generalized s-KKM type theorem Finitely continuous topological space FC-closed value Minimax inequalities
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Some Remarks for the Relationships between the Generalized Bernoulli and Euler Polynomials 被引量:1
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作者 LUO Qiu-ming GE Shu-mei 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第1期16-22,共7页
In this paper,we prove the Srivastava-Pint'er's addition theorems(see Applied Mathematic Lett.17(2004),375-380) by applying the another methods.We also provide some analoges of these addition theorems and dedu... In this paper,we prove the Srivastava-Pint'er's addition theorems(see Applied Mathematic Lett.17(2004),375-380) by applying the another methods.We also provide some analoges of these addition theorems and deduce the corresponding special cases. 展开更多
关键词 Bernoulli polynomials and numbers Euler polynomials and numbers generalized Bernoulli polynomials and numbers generalized Euler polynomials and numbers generating functions srivastava-Pinter's addition theorem
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HYPERCYCLICITY, SUPERCYCLICITY AND GENERALIZED RAKOEVIC'S PROPERTY
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作者 Mohamed AMOUCH Youness FAOUZI 《Acta Mathematica Scientia》 SCIE CSCD 2017年第2期503-510,共8页
A Banach space operator satisfies generalized RakoSevi5's property (gw) if the complement of its upper semi B-Weyl spectrum in its approximate point spectrum is the set of eigenvalues of T which are isolated in the... A Banach space operator satisfies generalized RakoSevi5's property (gw) if the complement of its upper semi B-Weyl spectrum in its approximate point spectrum is the set of eigenvalues of T which are isolated in the spectrum of T. In this note, we characterize hypecyclic and supercyclic operators satisfying the property (gw). 展开更多
关键词 Weyl's and ^-Weyl's theorems generalized Weyl's and generalized a^Weyl's theorems Browder's and a-Browder's theorems generalized Browder's and generalized a-Browder's HYPERCYCLICITY supercyclicity Rakocevic's property
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Biased Random Number Generator Based on Bell's Theorem
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作者 谭勇刚 胡要花 杨海峰 《Chinese Physics Letters》 SCIE CAS CSCD 2016年第3期5-8,共4页
We propose a biased random number generation protocol whose randomness is based on the violation of the Clauser Home inequality. Non-maximally entangled state is used to maximize the Bell violation. Due to the rotatio... We propose a biased random number generation protocol whose randomness is based on the violation of the Clauser Home inequality. Non-maximally entangled state is used to maximize the Bell violation. Due to the rotational asymmetry of the quantum state, the ratio of Os to ls varies with the measurement bases. The experimental partners can then use their measurement outcomes to generate the biased random bit string. The bias of their bit string can be adjusted by altering their choices of measurement bases. When this protocol is implemented in a device-independent way, we show that the bias of the bit string can still be ensured under the collective attack. 展开更多
关键词 BELL in TEsT IT In Biased Random Number generator Based on Bell’s theorem of Is that on
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Uncertainty Principles for the Generalized Fourier Transform Associated with Spherical Mean Operator
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作者 Hatem Mejjaoli Youssef Othmani 《Analysis in Theory and Applications》 2013年第4期309-332,共24页
The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
关键词 generalized Fourier transform Hardy's type theorem Cowling-Price's theorem Beurling's theorem Miyachi's theorem Donoho-stark's uncertainty principle.
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Existence of Solutions to a Generalized System
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作者 Yali Zhao Lin Xing Jia Tao 《Applied Mathematics》 2012年第6期511-516,共6页
In this paper, we introduce a generalized system (for short, GS) in real Banach spaces. Using Brouwer’s fixed point theorem, we establish some existence theorems for the generalized system without monotonicity. Furth... In this paper, we introduce a generalized system (for short, GS) in real Banach spaces. Using Brouwer’s fixed point theorem, we establish some existence theorems for the generalized system without monotonicity. Further, we extend the concept of C-strong pseudomonotonicity and extend Minty’s lemma for the generalized system. And using the Minty lemma and KKM-Fan lemma, we establish an existence theorem for the generalized system with monotonicity in real reflexive Banach spaces. As the continuation of existing studies, our paper present a series of extended results based on existing corresponding results. 展开更多
关键词 generalized system C-strong PsEUDOMONOTONICITY Brouwer’s Fixed POINT theorem Hemicontinuous MAPPING
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Investigation of Probability Generating Function in an Interdependent <i>M/M/</i>1:(∞;GD) Queueing Model with Controllable Arrival Rates Using Rouche’s Theorem
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作者 Vishwa Nath Maurya 《Open Journal of Optimization》 2012年第2期34-38,共5页
Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rate... Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rates-slower and faster as per controllable arrival policy. Keeping in view the general trend of interdependent arrival and service processes, it is presumed that random variables of arrival and service processes follow a bivariate poisson distribution and the server provides his services under general discipline of service rule in an infinitely large waiting space. In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into consideration;which may be helpful for mathematicians and researchers for establishing significant performance measures of the model. Moreover, for the purpose of high-lighting the application aspect of our investigated result, very recently Maurya [1] has derived successfully the expected busy periods of the server in both cases of slower and faster arrival rates, which have also been presented by the end of this paper. 展开更多
关键词 Interdependent QUEUEING Model BIVARIATE Poisson Process Controllable Arrival Rates Probability generating Function Laplace Transform Rouche’s theorem Performance Measures
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Deriving some quantum optical identities using the general ordering theorem
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作者 Farid Shhandeh Mohammad Reza Bazrafkan Elahe Nahvifard 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第11期233-236,共4页
Using the newly introduced general ordering theorem by Sh/ihandeh and Bazrafkan, we derive and generalize some quantum optical identities and give their applications.
关键词 s-ordered expansion of operators general ordering theorem
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Power Balance Theorem of Frequency Domain and Its Application 被引量:10
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作者 Binghua Huang Guangming Li Huijie Liu 《Journal of Modern Physics》 2014年第12期1097-1108,共12页
This paper proves a power balance theorem of frequency domain. It becomes another circuit law concerning power conservation after Tellegen’s theorem. Moreover the universality and importance worth of application of t... This paper proves a power balance theorem of frequency domain. It becomes another circuit law concerning power conservation after Tellegen’s theorem. Moreover the universality and importance worth of application of the theorem are introduced in this paper. Various calculation of frequency domain in nonlinear circuit possess fixed intrinsic rule. There exists the mutual influence of nonlinear coupling among various harmonics. But every harmonic component must observe individually KCL, KVL and conservation of complex power in nonlinear circuit. It is a lossless network that the nonlinear conservative system with excited source has not dissipative element. The theorem proved by this paper can directly be used to find the main harmonic solutions of the lossless circuit. The results of solution are consistent with the balancing condition of reactive power, and accord with the traditional harmonic analysis method. This paper demonstrates that the lossless network can universally produce chaos. The phase portrait is related closely to the initial conditions, thus it is not an attractor. Furthermore it also reveals the difference between the attractiveness and boundedness for chaos. 展开更多
关键词 tellegens theorem HARMONIC CONsERVATIVE system CHAOs LOssLEss CIRCUIT
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SOME PROPERTIES OF SOLUTIONS OF ONE-DIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH GENERAL COEFFICIENTS
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作者 丁晓东 《Journal of China Textile University(English Edition)》 EI CAS 1995年第1期75-80,共6页
In this paper, the one-dimensional time-homogenuous lto’s stochastic differential equations, which have degenerate and discontinuous diffusion coefficients, are considered. The non-confluent property of solutions is ... In this paper, the one-dimensional time-homogenuous lto’s stochastic differential equations, which have degenerate and discontinuous diffusion coefficients, are considered. The non-confluent property of solutions is showed under some local integrability condition on the diffusion and drift coefficients. The strong comparison theorem for solutions is also established. 展开更多
关键词 stochastic differential equation sTRONG comparison theorem non-confluent generalized Ito’s rule.
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The Power of Group Generators and Relations: An Examination of the Concept and Its Applications
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作者 Tiancheng Zhou 《Journal of Applied Mathematics and Physics》 2018年第11期2425-2444,共20页
This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtap... This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtaposing letters in a set. Taking that as basis, several fundamental results related to free groups, such as Dyck’s Theorem, are proven. Then, the paper highlights three creative applications of the concept in classifying finite groups of a fixed order, representing all dihedral groups geometrically, and analyzing knots topologically. All three applications are of considerable significance in their respective topic areas and serve to illustrate the advantages and certain limitations of the approach flexibly and comprehensively. 展开更多
关键词 generators and RELATIONs Free GROUP Dyck’s theorem Dihedral GROUP Presentation Classification of Finite GROUPs (Application) Realizing Dihedral GROUPs Geometrically (Application) KNOT GROUP (Application)
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离散对象的计数
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作者 冯积社 徐守军 潘卓 《纯粹数学与应用数学》 2024年第1期117-133,共17页
本文从集合概念出发,分别就重集,全序和偏序集,计数基本原理等内容,汇总了线状和环状的排列与组合,整数分析对应的标准和半标准杨表计数的常用计数解题的方法和技巧.随后从生成函数,格路计数和Polya计数定理等方面,用实例的方法说明它... 本文从集合概念出发,分别就重集,全序和偏序集,计数基本原理等内容,汇总了线状和环状的排列与组合,整数分析对应的标准和半标准杨表计数的常用计数解题的方法和技巧.随后从生成函数,格路计数和Polya计数定理等方面,用实例的方法说明它们在离散对象计数方面的应用.最后,通过求解化学中同分异构体计数问题的简短编程,介绍了计算机辅助软件Maple在快速高效求解离散对象计数问题方面的作用. 展开更多
关键词 离散对象 计数 生成函数 格路计数 Polya计数定理
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S-粗集的副集α-生成与α-生成定理 被引量:18
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作者 王洪凯 胡海清 《山东大学学报(理学版)》 CAS CSCD 北大核心 2004年第1期9-14,共6页
给出了S 粗集的副集α 生成 ,副集的集 -生成概念 ;给出了副集α 生成特性 ,副集的集 -生成特性 ;提出了副集的α 生成定理 ,副集的集 -生成定理 ;给出了S 粗集的属性非空原理 ,S 粗集的属性基数原理 .
关键词 s-粗集 副集 α-生成 α-生成定理 集-生成 集-生成定理 属性非空原理 属性基数原理
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基于广义Tellegen定理的静态电压稳定实用判据 被引量:1
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作者 鲁宝春 王成山 +1 位作者 郭志忠 柳焯 《天津大学学报(自然科学与工程技术版)》 EI CAS CSCD 北大核心 2001年第6期727-729,共3页
提出一种快速判定静态电压稳定的新方法 .基于广义 Tellegen定理推导出静态电压稳定基本判据 ;通过分析该静态电压稳定判据的物理意义 ,给出了电压稳定判据 .研究结果表明 ,该判据简捷、实用 ,能为在线电压稳定分析与控制提供依据 .
关键词 电压稳定 电压稳定判据 广义tellegen定理 静态电压 网络拓扑结构 电力系统
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基于广义Tellegen定理的小扰动定理在含光伏源的电力系统潮流算法中的应用研究 被引量:1
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作者 冮明颖 鲁宝春 +1 位作者 姜丕杰 于常武 《电力系统保护与控制》 EI CSCD 北大核心 2015年第18期31-36,共6页
广义Tellegen定理与物理系统属性无关,只与物理系统所建立的数学模型有关,因而被广泛地应用于电力系统中。考虑光伏并网影响因素,将光伏系统视为PQ节点,在电流注入潮流模型的基础上,利用小扰动定理建立基于广义Tellegen定理的修正方程... 广义Tellegen定理与物理系统属性无关,只与物理系统所建立的数学模型有关,因而被广泛地应用于电力系统中。考虑光伏并网影响因素,将光伏系统视为PQ节点,在电流注入潮流模型的基础上,利用小扰动定理建立基于广义Tellegen定理的修正方程。利用新的修正方程,以引入光伏源的IEEE30节点测试系统为例进行潮流计算。算例分析表明,该算法的迭代次数及潮流计算速度均有所改善,同时也表明了广义Tellegen定理在含光伏源系统中同样具有重要的应用价值。 展开更多
关键词 广义tellegen定理 小扰动定理 潮流计算
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S-粗集的副集α-生成粒度 被引量:4
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作者 王洪凯 胡海清 《山东大学学报(理学版)》 CAS CSCD 北大核心 2004年第3期32-36,41,共6页
利用S-粗集理论,给出单向副集As(Xσ)的α-生成粒度,双向副集As(X*)的α-生成粒度等概念;提出单向副集As(Xσ)的α-生成粒度特性定理,双向副集As(X*)的α-生成粒度特性定理;给出副集α-生成粒度的存在背景及在风险投资决策估计中的应用.
关键词 s-粗集 副集 As(X°)的α-生成粒度 As(X°)的α-生成粒度定理 As(X^*)的α-生成粒度 As(X^*)的α-生成粒度定理
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函数S-粗集,函数粗集与信息系统规律拆分-合成 被引量:13
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作者 史开泉 《计算机科学》 CSCD 北大核心 2010年第10期1-10,共10页
给出函数单向S-粗集(function one direction singular rough sets)、函数单向S-粗集对偶(dual of function one direction singular rough sets)、函数双向S-粗集(function two direction singular rough sets)与函数粗集(function rou... 给出函数单向S-粗集(function one direction singular rough sets)、函数单向S-粗集对偶(dual of function one direction singular rough sets)、函数双向S-粗集(function two direction singular rough sets)与函数粗集(function roughsets)。它们都是把函数概念引入到S-粗集中,改进S-粗集得到的。函数粗集是把函数概念引入到Z.Pawlak粗集中,改进Z.Pawlak粗集得到的。函数单向S-粗集、函数单向S-粗集对偶、函数双向S-粗集是函数S-粗集的三类形式。给出函数S-粗集与S-粗集的关系;给出函数粗集与Z.Pawlak粗集的关系;给出函数S-粗集与函数粗集的关系。利用这些结果,给出函数的区间离散与有限元素集的生成、函数离散-元素集合生成原理;给出函数S-粗集生成的信息规律、函数等价类动态特性-属性补充与删除原理;给出数据拆分-合成原理、信息规律动态拆分-合成的属性特征;给出信息规律动态拆分-合成不变性原理;利用这些概念与结果,给出信息规律拆分-合成与信息图像嵌入-分离的应用,给出嵌入信息图像的分离-辨识。函数S-粗集、函数粗集是粗集理论与应用研究中的一个新的研究方向。 展开更多
关键词 函数s-粗集 函数粗集 关系定理 信息规律生成 拆分-合成原理 信息图像嵌入 应用
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一种基于广义Tellegen定理的潮流快速算法
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作者 姜丕杰 郑率 +3 位作者 李宝国 冮明颖 程海军 鲁宝春 《辽宁工业大学学报(自然科学版)》 2014年第1期11-15,共5页
为了提高电力系统潮流解算效率,给出了基于广义Tellegen定理的潮流快速算法。该方法以电力网络节点电压方程为基础,建立了基于广义Tellegen定理的伴随网络方程,并根据广义Tellegen定理差形式,形成了简捷的潮流迭代方程。在迭代求解过程... 为了提高电力系统潮流解算效率,给出了基于广义Tellegen定理的潮流快速算法。该方法以电力网络节点电压方程为基础,建立了基于广义Tellegen定理的伴随网络方程,并根据广义Tellegen定理差形式,形成了简捷的潮流迭代方程。在迭代求解过程中,简化了求解过程,缩短了计算时间;同时,在计算中分别给出了PQ节点、PV节点及平衡节点的处理方法和计算公式。仿真结果表明,本文算法与保留非线性电流注入型算法相比,在保持计算精度和收敛性不变的情况下,提高了潮流计算速度。 展开更多
关键词 广义tellegen定理 潮流算法 伴随网络 节点电压方程
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